Sine Waves
The story of a waveform
The sine wave is the most basic sound there is, a pure fundamental without any harmonic overtones. It is the "atom" of sound, its most basic building block. According to the mathematics of the Fourier transform, any complex sound can be deconstructed (and reconstructed) into a manifold of individual sine waves. Additive synthesis makes use of the sine's fundamental purity, as does FM synthesis. The simple gives way to the complex.
The pure sine wave is an early theoretical, late practical invention, since as a sound it does not occur in the natural acoustic world. Only with the advent of electronic signal generation could the function be practically synthesized. Long before it was used in electronic music, it served as a test signal for electronic equipment. When composers like Stockhausen started making electronic music in the 1950s, dedicated synthesizers as we know them now did not exist yet. For sound generation, they relied on test oscillators made for scientific and military purposes.
As such, for techno-historical reasons, the sine wave became the sound that defined early electronic music. But its characteristics also suited the musical ideology of electronic music's early practitioners. For the composers of the Studio WDR, the sine represented a whole new ideal of music: Scientific exactness, technical mastery over nature and absolute control over the sonic material. The sine wave brought together serialism, electronic music, post-war technoscience and the military-industrial complex. In stark contrast to the Studio WDR, it is telling that Pierre Schaeffer never really made use of the sine wave. He was interested in listening to the acoustic world, recording, sampling and playing with its rich and complex murmurs. The sine's alien purity had no place in his vision for musique concrète. We can thus see how this most simple sound became a central point of contention in the war over what the future of music should look like.
Inevitably, the sound of the sine also made its way into the repertoire of popular culture, most notably in early science-fiction TV and film. The frequent use of sine oscillators and the sine-like Theremin cemented its cultural-semiotic association with technology and the future. It is worth remembering that the fact that R2D2 speaks in sine-like beeps is itself a cultural contingency — it could have also been any other sound. But these associations have become so entrenched that they are now irreversible. Robots and machines beep and bloop, that's just how it is. Even in our everyday life, the sine beep remains the basic language of technical objects. My microwave and air fryer speak to me in sine waves. When we hear a sine tone in a non-musical context, we usually start looking for some kind of machine or technical object that is demanding our attention.
In popular music, the sine wave has come to inhabit many different, sometimes contradictory functions and meanings. Techno makes use of its sci-fi associations to construct dark, machinic and futuristic soundscapes, for example in early Sähkö records. But in early 00's trance and progressive house, it is often used as an emotional, mourning sound. Despite — or perhaps because of — its simplicity, the sine can signify both an "inhuman" absence of emotion and a strong presence of emotion, depending on the context it is used in. In either case, there is always something excessive to it. With all of its energy concentrated on a single frequency, the sine has a special kind of power. It is a sound that makes its presence known, and demands our attention.
In 90s UK dance music, producers started — echoing the pioneers’ use of test equipment — abusing the sine test-tone of their Akai samplers to create particularly heavy bass-lines. Later, with dubstep, the pure sine wave sub-bass became synonymous with an entire genre. When americanized "Brostep" started trading in sines for midrange-y screams and growls, this was for many a betrayal of the genre's original aim to "meditate on bass weight". Just as it did in the 1950s, the sine again occupied a center stage in musical frequency politics.
One particularly fascinating aspect of the sine is the way it changes its phenomenological characteristics when transposed across the frequency spectrum, despite always remaining the same function. Under five hertz, it is one of the most popular control signals ("LFO"). There is something about its smooth, symmetrical shape that is just pleasing when employed as a modulation signal. At forty hertz, it is a deep, bassy tone felt more in the gut than the ears. In the lower midrange, we begin to move from the gut to the ear. Crossing a thousand hertz, we approach the sound we would call a "beep". For evolutionary speech-processing reasons, our ears are most sensitive in the two to four thousand hertz range. Beeps in this range are the kind that make themselves known, instinctively make us turn when the microwave beeps.
Over four thousand hertz, the sine increasingly begins to take on a strange, ghostly presence. But that makes it no less corporeal. A very high frequency sine wave is often perceived as shrill, disturbing and unnerving. It is a sound many people hear in perpetuity — the sound of their tinnitus. When I lay down in a silent room, I do not hear silence. I am always accompanied by two ringing, beeping, sine-like tones. For some, this is intolerable; it is said to have driven people to suicide. Like many, I personally have made peace with these strange tones that are a part of me, always slowly undulating and shifting in amplitude and frequency. I have even spoken to people who say they have to come to appreciate the ghostly, sine-like tones in their ears.
The case of tinnitus highlights the ambiguous, manifold character of the sine wave. It can enact both violence and healing. A great musical example for these complex tensions is the Japanese artist Sachiko M's album Bar さちこ.
It consists of nothing but a single — later joined by another — sustained sine tone. Listening to it in its entirety will almost certainly drive many people insane, but others might find themselves reaching a kind of nirvana. In every culture, this ambiguous place between insanity and salvation, violence and healing, has a name: It is what we call the sacred.